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Mathematics

OpenStudy (anonymous):

use logarithmic differentiation to find y=x^(x+2)

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myininaya (myininaya):

\[\ln(y)=\ln(x^{x+2}) =>\ln(y)=(x+2)\ln(x)\]

myininaya (myininaya):

take derivative of both sides

myininaya (myininaya):

\[\frac{y'}{y}=(1+0)\ln(x)+(x+2)\frac{1}{x}\]

myininaya (myininaya):

now multiply both sides by y

myininaya (myininaya):

\[y'=y[\ln(x)+\frac{x+2}{x}]=x^{x+2}[\ln(x)+\frac{x+2}{x}] \]

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